Reinforcement Learning for Integer Programming: Learning to Cut

TL;DR

This paper demonstrates that reinforcement learning can significantly improve the efficiency of integer programming solvers by intelligently selecting cutting planes, outperforming traditional heuristics and generalizing across larger instances and different problem classes.

Contribution

The authors develop a deep RL approach for adaptive cut selection in IP, enhancing solver performance and generalization beyond human-designed heuristics.

Findings

RL-based cut selection outperforms heuristics across various IP tasks

The trained RL agent generalizes to 10X larger instances

Improves the effectiveness of cutting plane methods in Branch-and-Cut algorithms

Abstract

Integer programming (IP) is a general optimization framework widely applicable to a variety of unstructured and structured problems arising in, e.g., scheduling, production planning, and graph optimization. As IP models many provably hard to solve problems, modern IP solvers rely on many heuristics. These heuristics are usually human-designed, and naturally prone to suboptimality. The goal of this work is to show that the performance of those solvers can be greatly enhanced using reinforcement learning (RL). In particular, we investigate a specific methodology for solving IPs, known as the Cutting Plane Method. This method is employed as a subroutine by all modern IP solvers. We present a deep RL formulation, network architecture, and algorithms for intelligent adaptive selection of cutting planes (aka cuts). Across a wide range of IP tasks, we show that the trained RL agent significantly outperforms human-designed heuristics, and effectively generalizes to 10X larger instances and across IP problem classes. The trained agent is also demonstrated to benefit the popular downstream application of cutting plane methods in Branch-and-Cut algorithm, which is the backbone of state-of-the-art commercial IP solvers.